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The Solow Model and the Steady State - YouTube
Channel: Marginal Revolution University
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- [Alex] Welcome back.
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Let's continue our exploration
of the Solow Growth Model.
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In our last video, we covered
how physical capital faces
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the iron logic
of diminishing returns.
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Now let's turn
to another unfortunate aspect
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of physical capital: capital rusts.
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Roads get potholes
and need to be repaired,
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tools wear out, trucks break down.
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In short, we say
that capital depreciates.
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Now let's put the amount of capital
on the horizontal axis
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and the amount of depreciation
on the vertical axis.
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We can then model
the relationship like this.
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Depreciation increases
at a constant rate
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as the capital stock increases.
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The more capital you have,
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the more capital depreciation
you have.
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Now let's add a new aspect
to our model.
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Where does the money
for capital accumulation come from?
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>From savings and investment.
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When we create economic output,
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we can either
consume it or save it.
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What we don't consume can be saved
and invested in new capital.
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So suppose we invest
a constant fraction of our output.
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Let's say we devote
3 of every 10 units of output
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or 30% of output to investment.
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We can now add
an investment curve to our graph.
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It'll mimic the shape
of the output line
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since investment is just
a constant fraction of output.
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Notice that our first units
of capital -- they're very productive
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and so they create a lot of output
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and thus also a lot of investment.
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But as we add
more and more units of capital,
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we get less output
and also less investment.
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That's the iron logic
of diminishing returns once again.
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Now let's put investment
and depreciation on the same graph.
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Depreciation is growing
at the same rate
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as the capital stock grows.
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Each new unit of capital creates
an equal amount of depreciation.
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Now notice that when investment
is greater than depreciation,
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that means the capital stock
must be growing.
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We're adding more units of capital
than are depreciating.
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But as the capital stock grows –
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investment and depreciation --
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they're on a crash course
to intersect.
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When this happens,
we've reached what is called
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the Steady-State Level of Capital.
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The steady-state is the key
to understanding the Solow Model.
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At the steady-state, an investment
is equal to depreciation.
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That means that
all of investment is being used
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just to repair and replace
the existing capital stock.
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No new capital is being created.
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Now remember, we've assumed
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that all the other variables
in the model -- they're not changing.
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So if the capital stock
isn't growing, nothing is growing.
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In other words, when we reach
the Steady-State Level of Capital
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we've also reached
the Steady-State Level of Output.
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Now suppose you ended up
on the other side
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of the steady-state point --
over here.
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You'd find that depreciation
is greater than investment.
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That means some
of the capital stock needs repair,
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but there isn't enough investment
to do all of the needed repairs,
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so the capital stock shrinks,
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pushing you back
towards the steady-state.
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So to the left of the steady-state
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we have investment
greater than depreciation
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and the capital stock is growing.
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To the right of the steady-state
we have the opposite --
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depreciation is greater
than investment,
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and the capital stock --
it's shrinking.
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Either way, we always end up
moving towards the steady-state.
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Now let's go back
to our earlier example
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of Germany after the end
of World War II.
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Since the capital stock is low,
it's also very productive
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and we get a lot of output
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from the first new roads
and factories after the war.
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We've already mentioned that point.
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But in addition, we now see
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that when the capital stock
is very productive
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and producing a lot of output,
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we will also be producing
a lot of investment.
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So in the next period
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the capital stock will be
even bigger than before
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and we'll get even more output.
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Plus, since
the capital stock is low,
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we don't have much depreciation
to take care of.
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So with the investment,
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it will mostly be
generating new capital,
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not replacing old capital.
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Now over time, however,
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both of these forces -- they weaken.
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The returns to capital diminish
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and depreciation eats up
more and more of investment.
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A country with a lot of roads,
and bridges and factories --
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it's doing well,
but it also has to invest a lot
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just to maintain all those roads
and bridges and factories.
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And this is exactly what we saw
in Germany and Japan
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after World War II.
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Growth rates started out very high,
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but as those countries caught up,
growth rates declined.
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Now perhaps our friend K still has
one more trick up his sleeve
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to get the economy growing.
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What if we started
to save more of our output?
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A higher savings rate shifts
the investment curve up like this.
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Now investment is higher
than depreciation,
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so we're adding
to the capital stock
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and the economy is back to growing.
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However, you can see
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that the same dynamic
exists as before.
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The iron logic
of diminishing returns means
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that we'll again end up
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at a new steady-state level
of capital.
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The higher savings rate --
it spurs growth for a time
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and it does increase
the steady-state level of output.
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But, at the new steady-state,
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investment once again
equals depreciation
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and we get zero economic growth.
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Accumulation of physical capital
can only generate temporary growth.
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In our next video,
we'll take a look
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at how human capital
influences growth.
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- [Narrator] If you want
to test yourself,
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click "Practice Questions."
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Or, if you're ready to move on,
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you can click,
"Go to the Next Video."
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You can also visit MRUniversity.com
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to see our entire library
of videos and resources.
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